in a research study aimed to measure the most effective way to study, students are given a test on the material they reviewed. A group of ne15 was asked to take an exam after they read lecture summaries and after they watched and listened to lecture summaries. The researcher noticed that once a student took the test the first time, they were able to get through the exam faster the second time. What should the researcher have done to avoid this problem? a. Give the test at different hours of the day b. Create different test for the students c. Give the test in different languages d. Switch the order of study methods for the participants before the test

The Answers are:

(a) ∂f/∂x = 2xy + 6x + 4y

   ∂f/∂y = x² + 4x

(b) ∂f/∂x = 0

   ∂f/∂y = 2

(c) ∂f/∂x = (2x)/(x² + y)

   ∂f/∂y = 1/(x² + y)

To find the partial derivatives of the given functions, we differentiate the function with respect to the specified variable while treating other variables as constants.

(a) For f(x, y) = x²y + 3x² + 4xy - 5:

∂f/∂x = 2xy + 6x + 4y

∂f/∂y = x² + 4x

(b) For f(x, y) = ²² + 2y:

∂f/∂x = 0

∂f/∂y = 2

(c) For f(x, y) = ln(x² + y):

∂f/∂x = (2x)/(x² + y)

∂f/∂y = 1/(x² + y)

In summary:

(a) ∂f/∂x = 2xy + 6x + 4y

   ∂f/∂y = x² + 4x

(b) ∂f/∂x = 0

   ∂f/∂y = 2

(c) ∂f/∂x = (2x)/(x² + y)

   ∂f/∂y = 1/(x² + y)

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Answer:

<E

Step-by-step explanation:

The points need to be in order.  P is the second to the last on the list and so is E.

Answer:

-31.5

Step-by-step explanation:

36(0.25)+ 42(-1)-18(0.25)+6
9-42-4.5+6

=-31.5

Answer:

8: 1721 m

9: 1173 m

Step-by-step explanation:

8:

\(d = v_{i} t + \frac{1}{2}at^{2}\)

because initial velocity is 0:

\(d = \frac{1}{2} at^{2} = \frac{1}{2}(3.2m/s^2)(32.8 s)^2 = 1721.344 m\)

9:

\(v_f^2 = v_i^2 + 2ad\)

because velocity initial is 0:

\(v_f^2 = 2ad\)

\(d = \frac{v_f^2}{2a} = \frac{(88m/s)^2}{2(3.3 m/s^2)} = 1173.3333 m\)

Answer:

do it youself

Step-by-step explanation:

Answer 5 ft 4 in

Step-by-step explanation:

2 1/2 + 2 1/2=5 + 4 inches

Answer:

56 degrees

Step-by-step explanation:

Hello there!

Remember the sum of the angles in a triangle is equal to 180

so to find the missing angle we subtract the given angles from 180

180 - 34 - 90 = 56

so we can conclude that the measure of the missing angle is 56 degrees

Note: the little square at the bottom left of the triangle indicates that the angle is a right angle. The measure of a right angle is 90 degrees so thats where the 90 came from

Answer:

hope it help you

Answer:

13, 5

Step-by-step explanation:

First, we find the common difference.

d = 29 - 37 = -8

Now we add -8 to the last term to find the next term.

21 + (-8) = 13

13 + (-8) = 5

Answer: 13, 5

The number of matchsticks that each side of the biggest triangle contains is; 137 matchsticks

We know that for a diagram to be a triangle, then two smallest sides must not be greater than the third side.

Now, if there are 273 matchsticks, then the greatest side of the triangle must not be less than 273/2 = 136.5 ≈ 137

Thus, the largest side will have at least 137 matchsticks

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Answer:

All natural numbers are whole numbers

Step-by-step explanation:

Step-by-step explanation:

12,000 views = 4 hours

=> 30,000 views = 4 * (30000/12000) = 10 hours.

Hence it will take 10 hours.

Answer:

10

Step-by-step explanation:

Since we know every 4 hours the vid recieves 12,000 views, we divide 12,000 by 4 to see how many views it recieves in 1 hour. We get 3,000. So 3,000 views every hour. Divide 30,000 by 3,000, to get 10 hours.

Answer:

you only have to flip the inequality if you you are divide or multiplying by a negative

The object represented by h(t) = -4.9t² + 40t + 20 would take 4.082 seconds to reach it's maximum height.

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

The height (h) is represented by:

h(t) = -4.9t² + 40t + 20

The maximum height is at h'(t) = 0, hence:

h'(t) = -9,8t + 40

-9.8t + 40 = 0

t =  4.082

The object represented by h(t) = -4.9t² + 40t + 20 would take 4.082 seconds to reach it's maximum height.

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Answer:

-7,-6,-3.these are the vertices

Answer: B. 200ft

Step-by-step explanation:

Pythagorean theorem so a^2+b^2+c^2 or 120^2+160^2=c^2 where c is the value for the diagonal so solving for c to get 200

FORMULA FOR COMPOUND INT. = A = P ( 1 + \(\frac{R}{100}\))\(^{n}\)

= P = 2000, R = \(\frac{5}{12}\) ( as it is compounded monthly ), N= 8 × 12 = 96

= A = 2000 \((\) 1 + \(\frac{5}{1200}\) \()^{96\\}\) = \(\frac{2000}{1}\) × (\(\frac{1205}{1200}\)) \(^{96}\)

= 2981.17

Answer:

600

Step-by-step explanation:

V = l * w * h

V = 10 * 3 * 20

V = 600

Answer:

V = 600 cm³

Step-by-step explanation:

The volume (V) of a cuboid is calculated as

V = lbh ( l is length, b is breadth, h is height )

Here l = 10, b = 3 , h = 20 , then

V = 10 × 3 × 20 = 600 cm³

Answer:

The answer to this question would be B

For the equation x^3 + 27y^4 = In  y' at (-3, 1) is -27/107 by using implicit differentiation y' = 3x^2 / (y - 108y^3).

To find y' using implicit differentiation and then evaluate y' at (-3,1) for the given equation x^3 + 27y^4 = ln(y), follow these steps:

1. Differentiate both sides of the equation with respect to x, remembering to apply the chain rule when differentiating with respect to y.

d/dx(x^3) + d/dx(27y^4) = d/dx(ln(y))

2. Apply the chain rule on the right-hand side:

3x^2 + 27(4y^3)(dy/dx) = (1/y)(dy/dx)

3. Solve for dy/dx (which is y'):

dy/dx(y - 108y^3) = 3x^2

y' = dy/dx = 3x^2 / (y - 108y^3)

4. Evaluate y' at (-3, 1):

y'(-3, 1) = 3(-3)^2 / (1 - 108(1)^3)

y'(-3, 1) = 27 / (-107)

So, y' = 3x^2 / (y - 108y^3), and y'(-3, 1) = -27/107.

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Answer:

x =5

Step-by-step explanation:

c = 5√2

a = x

b = x

Formula

x^2 + x^2 = c^2                    Combine the x^2

Solution

2x^2 = (5√2)^2                    Expand the right side

2x^2 = 2*25                         Divide both sides by 2

x^2 = 25                               Take the square root of both sides.

x = 5

Answer:

47.62 cm

Step-by-step explanation:

ABCD is a rhombus. Each side measures 15 cm.

m<A = 60°.

Here are some properties of a rhombus:

Opposite angles of a rhombus are congruent.

m<C = m<A = 60°

m<ADC = m<ABC

The sum of the measures of the interior angles of a quadrilateral is 360°.

The diagonals are perpendicular bisectors of each other.

m<A + m<C + m<ADC + m<ABC = 360°

60° + 60° + 2m<ADC = 360°

2m<ADC = 240°

m<ADC = 120°

Each diagonal of a rhombus bisects a pair of congruent, opposite angles.

m<ADB + m<CDB = m<ADC

m<ADB = m<CDB

m<ADB + m<ADB = 120°

m<ADB = 60°

Triangle ABD had two angles, <A and <ADB, that measure 60°. Therefore, the third angle, <ABD also measures 60°. That makes triangle ABD an equilateral triangle.

Draw segment AT.

T is the midpoint of BD. The segment AT is the perpendicular bisector of segment BD. Triangle ATD is a 30-60-90 triangle.

Using the ratio of the lengths of the sides of a 30-60-90 triangle, we can calculate the length of AT which is the radius of circle A.

TD : AT : AD

1    : √3 :   2

AD = 15 cm

TD = AD/2

AT = √3 × TD

AT = (AD√3)/2

AT = 7.5√3 = 12.99

AQ = 12.99

perimeter = QD + PB + m(arc)PTQ + BC + CD

perimeter = (15 - 12.99) + (15 - 12.99) + 60°/360° × 2π(12.99) + 15 + 15

perimeter = 47.62

Answer: perimeter = 47.62 cm

Answer:

a) 50 meters

b) 2354 meters

c) 12 seconds

d) 24.13 seconds

Step-by-step explanation:

Hello!

We need to really understand what the variables represent in this question. Given that t is time, and h is height, the time at which he shoots the bullet will be 0, as the bullet hasn't started traveling yet. This means that we can solve for the original height of the bullet by plugging in 0 for time in the equation.

Equation: \(h = -16t^2 + 384t + 50\)

Plug in 0 for t:

The height at which Lincoln shot the bullet is 50 meters.

We can also look at this graphically. The height of origin will simply be when the x-value (in this case t-value) is 0. That means it is the point at which the graph intersects the y-axis, known as the y-intercept.

Standard form of a Parabola: \(y = ax^2 + bx + c\)

The y-intercept is the "c" value.

Given our equation: \(h = -16t^2 + 384t + 50\)

The c-value is 50. This proves that the y-intercept is 50.

We want to find the highest point of the graph. To do that, we can find the vertex.

We can utilize the Axis of Symmetry (AOS) to find the Vertex.

First, find the AOS using the formula: \(AOS = -\frac{b}{2a}\)

Plug it into the formula:

Plug in 12 for t in the equation:

Therefore, the highest point of the bullet is 2354 meters.

We answered this in the last question. The t-value when h is at its highest is 12.

We have to solve for the values of t when h is 0 (when it touches the ground).

Set the equation to 0, and solve using the quadratic formula.

Quadratic formula: \(x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\)

We are only going to take the positive solution, as we can't have a negative time. The solution that doesn't work is called an extraneous solution.

It takes approximately 24.13 seconds for the bullet to hit the ground.

The normally distributed process has specifications of LSL = 75 and USL = 85 has a Cp of 2.22 , this process is capable and 0.08 defective parts can be expected per day.

To obtain the estimate of Cp, we first need to calculate the process capability index (Cpk) using the formula:

Cpk = min[(USL - mean) / (3 * standard deviation), (mean - LSL) / (3 * standard deviation)]

In this case, the sample mean is 80 and the sample standard deviation is 1.5, so:

Cpk = min[(85 - 80) / (3 * 1.5), (80 - 75) / (3 * 1.5)]
   = min[1.11, 1.11]
   = 1.11

To obtain Cp, we simply multiply Cpk by 2, since Cp = 2 * Cpk when the process is centered:

Cp = 2 * Cpk
  = 2 * 1.11
  = 2.22

Since Cp is greater than 1.0, this process is capable.

To calculate the expected number of defective parts per day, we need to know the proportion of parts that are defective.

Assuming that the process is centered, the proportion of parts that are defective can be estimated using the area under the normal distribution curve beyond the specification limits.

Since the process is normally distributed with mean 80 and standard deviation 1.5, we can use a standard normal distribution table to find the area beyond the limits:

Area beyond USL = P(Z > (USL - mean) / standard deviation) = P(Z > (85 - 80) / 1.5) = P(Z > 3.33) = 0.0004

Area beyond LSL = P(Z < (LSL - mean) / standard deviation) = P(Z < (75 - 80) / 1.5) = P(Z < -3.33) = 0.0004

So the proportion of parts that are defective is:

Proportion defective = 0.0004 + 0.0004 = 0.0008

To find the expected number of defective parts per day, we multiply this proportion by the number of parts produced per day:

Expected number of defective parts per day = 0.0008 * 100 = 0.08

So we would expect to see approximately 0.08 defective parts per day.

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Answer:

False.

Step-by-step explanation:

The RMS (Root Mean Square) value of a sine wave represents the equivalent DC voltage that would produce the same amount of power in a resistive load. However, the heat produced in a resistor is directly proportional to the square of the current passing through it (according to Joule's Law). In the case of an AC waveform, the current continuously changes direction, resulting in a time-varying power dissipation. Therefore, comparing the RMS value of an AC waveform to a DC voltage is not directly applicable in terms of heat produced in a resistor.

Answer:

-3

Step-by-step explanation:

The difference between 7-10 is -3. The minus sign is used because smaller number is subtracted from a larger number

Answer:

a) 7 numbers in term of n = n+1, n+2, n+3, n+4, n+5, n+6 and n+7

b) n+1+n+2+n+3+n+4+n+5+n+6+ n+7

= 7n+28

Step-by-step explanation:

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False. Using the specified side measures of 4.6, 2.7, and 1.9, a triangle cannot be created.

Any two side lengths must add up to more than the third side length in order for a triangle to have three sides. The two smaller sides in this scenario do not add up to be greater than the longest side because we can see that 1.9 + 2.7 = 4.6.

The Triangle Inequality Theorem stipulates that the total of any two triangle sides must be bigger than the third side. This isn't true in this case. Hence, a triangle cannot be formed with the side measurements provided.

In conclusion, it cannot be said that a triangle can have sides that measure 4.6, 2.7, and 1.9.

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Answer:

Okay done

Step-by-step explanation:

Answer:165degrees

Step-by-step explanation

Use formula N-2 × 180 N is the number of sides

24-2=22

22x180=3960 total

for each angle divide total by 24=165 degrees